Estimate the following quantities without using a calculator. Then find a more precise​ result, using a calculator if necessary. Discuss whether the approximation technique worked.

Answer:

C. 0 ≤ y ≤ 7

Step-by-step explanation:

Range is the interval of the numbers on the y-axis. The numbers go from y-value 1 to y-value 7. Since the circles at the ends are closed, this means 0 and 7 are included in the range, so ≤ is included instead of <.

The amount that the designer will have to pay in FICA taxes is:$3,978.

FICA taxes comprises of:

Social Security tax= 6.2%

Medicare tax= 1.45%

Hence:

FICA taxes=($52,000×6.2%)+($52,000×1.45%)

FICA taxes=$3,224+$754

FICA Taxes=$3,978

Therefore the amount that the designer will have to pay in FICA taxes is:$3,978.

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Answer:

84 degrees

Step-by-step explanation:

Angle A = 83 degrees

Angle B = x degrees

Angle C = 135 degrees

Angle CDE = 122 degrees

We know that the four inner corners of a quadrilateral should add up to 360 degrees. Two supplementary angles will add up to 180 degrees. Adjacent angles on a straight line will always be supplementary. Knowing this, just solve for <ADC and add that amount to <A and <C. Then, subtract that sum from 360 degrees.

<ADC = 180-122 = 58

58+83+135 = 276

360-276 = 84 degrees

Answer:

26

Step-by-step explanation:

(3a+2)/(a+4) = 8/3

(3a+2) = (8/3)(a+4)

(3a+2) = a*8/3 + 4*8/3

(3a+2) = 8a/3 + 32/3

3a - 8a/3 = 32/3 - 2

9a/3 - 8a/3 = 32/3 - 6/3

9a - 8a = 32 - 6

a = 26

Check:

(3*26 + 2) / (26+4) = 8/3

(78+2) / 30 = 8/3

80 / 30 = 8/3

Answer:

  y = 3x +5

Step-by-step explanation:

The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.

The desired equation in the given standard form will be ...

  3x -y = c . . . . . . for some new constant c

Note that we have kept the x-coefficient positive, and have negated the y-coefficient.

The new constant will make the equation true at the point (-1, 2):

  3(-1) -(2) = c = -5

So, the standard-form equation is ...

  3x -y = -5

The answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:

  3x -y +(y+5) = -5 +(y+5)

  3x +5 = y

  y = 3x +5

[tex]7x^2 = -12-5x\\\\7x^2 + 5x+12=0\\\\x=\frac{-5 \pm \sqrt{5^{2}-4(7)(12)}}{2(7)}\\\\\boxed{x=\frac{-5 \pm i \sqrt{311}}{14}}[/tex]

Answer:

Step-by-step explanation:

1) List the factors of each number.

Factors of 6 : 1, 2, 3, 6

Factors of 42 : 1, 2, 3, 6, 7, 14, 21, 42

Factors of 18 : 1, 2, 3, 6, 9, 18

2) Find the largest number that is shared by all rows above. This is the GCF.

GCF = 6

The value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

The expression is given as:

(38)-2⁢(13⋅38)3⁢(13)4.

Rewrite properly as:

(38) - 2 * ⁢(13 * 38) * 3 * ⁢(13) * 4.

Evaluate the products in the bracket

(38) - 2 * ⁢(494) * 3 * ⁢52

Further, expand

38 - 154128

Evaluate the difference

-154090

Hence, the value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

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Answer:

a & c

Step-by-step explanation:

Answer:

B) Point (1, 1) is a solution because it is one of the points on the line already graphed.

D) Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.

E) When the other line in the system is graphed, it will share all points with the line already graphed.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]y'' + \omega^2 y = 0[/tex]

has characteristic equation

[tex]r^2 + \omega^2 = 0[/tex]

with roots at [tex]r = \pm\sqrt{-\omega^2} = \pm|\omega|i[/tex], hence the characteristic solution is

[tex]y = C_1 e^{i|\omega|x} + C_2 e^{-i|\omega|x}[/tex]

or equivalently,

[tex]y = C_1 \cos(|\omega|x) + C_2 \sin(|\omega|x)[/tex]

With the given boundary conditions, we require

[tex]y(0) = 0 \implies C_1 = 0[/tex]

and

[tex]y'(\pi) = 0 \implies -|\omega| C_1 \sin(|\omega|\pi) + |\omega| C_2 \cos(|\omega|\pi) = 0[/tex]

With [tex]C_1=0[/tex], the second condition reduces to

[tex]|\omega| C_2 \cos(|\omega|\pi) = 0[/tex]

Assuming [tex]C_2\neq0[/tex] (because we don't want the trivial solution [tex]y=0[/tex]), it follows that

[tex]\cos(|\omega|\pi) = 0 \implies |\omega|\pi = \pm\dfrac\pi2 + 2n\pi \implies |\omega| = 2n\pm\dfrac12[/tex]

where [tex]n[/tex] is an integer. In order to ensure [tex]|\omega|\ge0[/tex], we must have [tex]n\ge1[/tex] if [tex]|\omega|=2n-\frac12[/tex], or [tex]n\ge0[/tex] if [tex]|\omega|=2n+\frac12[/tex].

Answer:

a

Step-by-step explanation:

The midline is at y=2.

Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.

This means the answer is a.

Answer:

(19-12):12*100 =

(19:12-1)*100 =

158.33333333333-100 = 58.33

Hello!

Simplifying :

⇒ 4m + 4m + 4m + 4m

⇒ 4(4m)

None of the above

Answer:

54

Step-by-step explanation:

the plot of land is an isosceles triangle, meaning two sides and angles are the same in value.

height (h)= 24

base (b)= 36

length (l)= 30

solution

find the area of triangle using area=half the product of the base and height.

A=1/2(36×24)

A= 216 square feet.

each tree needs 8 square feet

therefore using ratio and proportion,

1 tree= 8 square feet

x trees= 216 square feet

cross multiply and it'll be

216/8=x

therefore x= 54 trees

Answer: horizontal

Step-by-step explanation: there going across sideways and not up and down

Step-by-step explanation:

[tex]y = log_{4}( {x}^{4} ) [/tex]

Swap x and y.

[tex]x = log_{4}( {y}^{4} ) [/tex]

Solve for y.

[tex]x= 4 log_{4}(y) [/tex]

[tex] \frac{1}{4} x = log_{4}(y) [/tex]

[tex]4 {}^{ \frac{1}{4}x } = y[/tex]

So the inverse is

[tex]4 {}^{ \frac{x}{4} } = f {}^{ - 1} (x)[/tex]

The value of x in the equation is 2.

Indices singular index is a branch of algebra that deals with the power or exponent of variables.

Laws of indices help us to evaluate indicial expressions and equations.

Analysis:

[tex]4^{8-2x}[/tex] = 256

Here 4 is the base number while 8-2x is the exponent or index.

So for us to evaluate this, we need to write 256 in its index form having its base as 4 also.

so 256 in base 4 index form is [tex]4^{4}[/tex]

[tex]4^{8-2x}[/tex] = [tex]4^{4}[/tex]

since both sides have the same base number, we equate only their exponent

8-2x = 4

-2x = 4 - 8

-2x = -4

x = -4/-2 = 2

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Answer:

x = 2 , y = 7

Step-by-step explanation:

Since

y-3x = 1

y = 3x+1 - equation 1

2y-x = 12 - equation 2

Since we are using substitution method,

we will substitute equation 1 into equation 2.

[tex]2(3x + 1) - x = 12 \\ 6x + 2 - x = 12 \\ 5x + 2 = 12 \\ 5x = 12 - 2 \\ 5x = 10 \\ x = \frac{10}{5} \\ = 2[/tex]

Now we substitute x into equation 1 to find y.

[tex]y = 3(2) + 1 \\ = 6 + 1 \\ = 7[/tex]

Therefore x = 2, y = 7.

Answer:

1/x - 3

Step-by-step explanation:

The number is x.

The reciprocal of the number is 1/x.

3 is subtracted from the reciprocal of a number.

1/x - 3

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the equation of the line, with the info given.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

The formula used in this problem is,

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[tex]\bf{y-(-1)=3(x-3)[/tex] | simplify

[tex]\bf{y+1=3(x-3)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                         [tex]\bf{=y+1=3(x-3)}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

[tex]108 m^{2}[/tex]

Step-by-step explanation:

[tex]27\times4=108[/tex]

The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

An equation is an expression that shows the relationship between two or more numbers and variables.

Range is the difference between the maximum value and minimum value of a data set. Hence:

Range = Maximum - Minimum

Let us assume that the maximum point is 100 point and the minimum point is 20 point, hence:

Range = 100 - 20 = 80 points

The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

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The answers are

We have the cost function in this question to be

C(x) = 60x+300

We have the function of the revenue to be

Revenue = 100x−0.5x²

A. The formula for revenue function is given

revenue - cost

This is expressed as

= (100x−0.5x²)-60x+300

We have to collect like terms and open the equation above.

This given us:

B. when profit = 50$

We have p = 40x-0.5x²-300

50 = 40x-0.5x²-300

Multiply the two sides by 10

This gives

500 = 400x - 5x² - 3000

This gives a quadratic equation

5x² - 400x - 3500 = 0

To solve the equation you have to make use of a quadratic calculator.

This gives us the values

c. We have  P =  40x-0.5x²-300.

at P = 2500

2500  =  40x-0.5x²-300.

Multiply the equation by 10

25000 = 400x - 5x² - 3000

collect like terms

400x - 5x2 - 3000 +28000

400x -5x2 +28000

We have to take the discriminant

-400² - 4*5*28000

= -400000

The discriminant is negative hence it is not possible.

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Answer: 112.5 square cm

Step-by-step explanation:

The area of the rectangle is [tex](20)(9)=180[/tex] square cm.

The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.

So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.

Step-by-step explanation:

Answer :- Amount (after 11 years) = $4522.11

Step-by-step explanation:

a ) Solution,

[tex] = \frac{7}{8} \div \frac{9}{10} \\ [/tex]

[tex] = \frac{7}{8} \times \frac{10}{9} \\ [/tex]

[tex] = \frac{70}{72} \\ [/tex]

Change into lowest term....

[tex] = \frac{35}{36} \\ [/tex]

Answer:

27π cm² or 84.8 cm²

Explanation:

[tex]\sf Formula \ for \ area \ of \ sector = \dfrac{\theta}{360 } \ x \ \pi (radius)^2[/tex]

Shaded region angle: 360° - 90° = 270°

 Given radius: 6 cm

Applying formula:

[tex]\rightarrow \sf \dfrac{270}{360} \ x \ \pi (6)^2[/tex]

[tex]\rightarrow \sf 27\pi[/tex]

[tex]\rightarrow \sf 84.823 \ cm^2[/tex]

[tex]\rightarrow \sf 84.8 \ cm^2 \quad (rounded \ to \ nearest \ tenth)[/tex]

The total number of pies they made altogether is 100.

In order to determine this value, add the number of blueberry pies with the number of apple pies.  Addition is the mathematical operation that is used to determine the sum of two or more numbers.

The total number of pies = 55 + 45 = 100 pies

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